Matrix extensions of real orthogonal polynomials where first discussed back in 1949 by Krein [1]}, [2]}
and thereafter were studied sporadically until the last decade of the XX century, being some relevant papers [3]}, [4]}, [5]}.
Then, in 1984, Aptekarev and Nikishin, for a kind of discrete Sturm–Liouville operators, solved the corresponding scattering problem in [5]}, and found that the polynomials that satisfy a relation of the form
\(xP_{k}(x)&=A_{k}P_{k+1}(x)+B_{k}P_{k}(x)+A_{k-1}^{*}P_{k-1}(x),& k&=0,1,\dots ,\) 
